Common substring with shifts in b-ary expansions
Xin Liao, Dingding Yu · arXiv (Cornell University) · 2024
Denote by $S_n(x,y)$ the length of the longest common substring of $x$ and $y$ with shifts in their first $n$ digits of $b$-ary expansions. We show that the sets of pairs $(x,y)$, for which the growth rate of $S_n(x,y)$ is $α\log n$ with $0\le α\le \infty$, have full Hausdorff dimension.